\(=\frac{5}{x+2}+\frac{x}{x-2}-\frac{3x-14}{\left(x+2\right).\left(x-2\right)}=\frac{5x-10+x^2+2x-3x+14}{\left(x+2\right).\left(x-2\right)}=\frac{x^2+4x+4}{\left(x+2\right).\left(x-2\right)}=\frac{\left(x+2\right)^2}{\left(x-2\right).\left(x+2\right)}=\frac{x+2}{x-2}\)
3) \(\frac{1-x}{x+1}-\frac{3+2x}{x+1}=0\)
13) \(\frac{x+2}{x}-\frac{x^2+5x+4}{x\left(x+2\right)}=\frac{x}{x+2}\)
14) \(\frac{1}{x+1}-\frac{5}{x-2}=\frac{20}{\left(x+1\right)\left(2-x\right)}\)
16) \(\frac{x+5}{x-5}-\frac{x-5}{x+5}=\frac{20}{x^2-25}\)
17) \(\frac{3x+2}{3x-2}-\frac{6}{2+3x}=\frac{9x^2}{9x^2-4}\)
18) \(\frac{x-1}{x}+\frac{1}{x+1}=\frac{2x-1}{2x^2+2}\)
19) \(\frac{2}{x+1}-\frac{3x+1}{\left(x+1\right)}=\frac{1}{\left(x+1\right)\left(x-2\right)}\)
20) \(\frac{x+5}{3x-6}-\frac{1}{2}=\frac{2x-3}{2x-4}\)
Tính
\(\frac{5}{x+2}+\frac{x}{x-2}+\frac{3x-14}{4-x^2}\)
Mk cần gấp lắm. Giups mk nhanh nhé
bài 1: thực hiên phép tính
a, \(\frac{x^2}{x^2-x}\)- \(\frac{x^2}{x+1}\)-\(\frac{2x}{x^2-1}\)
b, \(\frac{4x^2-3x+5}{x^3-1}\)- \(\frac{1-2x}{x^2+x+1}\)- \(\frac{6}{x-1}\)
c, \(\frac{5}{2x^2+6x}-\frac{4-3x^2}{x^2-9}-3\)
d, \(\frac{5}{x+1}-\frac{10}{x-x^2-1}-\frac{15}{x^3+1}\)
bài 2: thực hiện phép tính
a, \(\frac{1}{x+1}-\frac{2x}{x-1}+\frac{x+3}{x^2-1}\)
b, \(\frac{2}{2x+1}-\frac{1}{2x-1}+\frac{2}{4x^2-1}\)
c, \(\frac{7}{8x^2-18}+\frac{1}{2x^2+3x}-\frac{1}{4x-6}\)
d, \(\frac{3x^2+5x+14}{x^3+1}+\frac{x-1}{x^2-x+1}-\frac{4}{x+1}\)
Bài 3: Giải các phương trình sau bằng cách đưa về dạng ax+b =0 :
a) \(\frac{3x-11}{11}-\frac{x}{3}=\frac{3x-5}{7}-\frac{5x-3}{9}\)
b) \(\frac{9x-0,7}{4}-\frac{5x-1,5}{7}=\frac{7x-1,1}{6}-\frac{5\left(0,4-2x\right)}{5}\)
c) \(\frac{5\left(x-1\right)+2}{6}-\frac{7x-1}{4}=\frac{2\left(2x-1\right)}{7}-5\)
d) \(14\frac{1}{2}-\frac{2\left(x+3\right)}{5}=\frac{3x}{2}-\frac{2\left(x-7\right)}{3}\)
\(\frac{1}{x^2-3x+3}+\frac{2}{x^2-3x+4}=\frac{6}{x^2-3x+5}\)
Giải các phương trình sau
a) \(\frac{7x-3}{x-1}=\frac{2}{3}\)
b) \(\frac{2\left(3-7x\right)}{1+x}=\frac{1}{2}\)
c) \(\frac{1}{x-2}+3=\frac{3-x}{x-2}\)
d) \(\frac{8-x}{x-7}-8=\frac{1}{x-7}\)
e) \(\frac{x+5}{x-5}-\frac{x-5}{x+5}=\frac{20}{x^2-25}\)
f)\(\frac{1}{x-1}+\frac{2}{x+1}=\frac{x}{x^2-1}\)
g) \(\frac{x}{2\left(x-3\right)}+\frac{x}{2\left(x+1\right)}=\frac{2x}{\left(x+1\right)\left(x-3\right)}\)
h)\(5+\frac{76}{x^2-16}=\frac{2x-1}{x+4}-\frac{3x-1}{4-x}\)
i) \(\frac{90}{x}-\frac{36}{x-6}=2\)
k) \(\frac{1}{x}+\frac{1}{x=10}=\frac{1}{12}\)
l) \(\frac{x+3}{x-3}-\frac{1}{x}=\frac{3}{x\left(x-3\right)}\)
m) \(\frac{3}{x+2}-\frac{2}{x-2}+\frac{8}{x^2-4}=0\)
n) \(\frac{3}{x+2}-\frac{2}{x-3}=\frac{8}{\left(x-3\right)\left(x+2\right)}\)
o)\(\frac{x}{2x+6}-\frac{x}{2x+2}=\frac{3x+2}{\left(x+1\right)\left(x+3\right)}\)
p) \(\frac{x}{x+1}-\frac{2x-3}{1-x}=\frac{3x^2+5}{x^2-1}\)
q) \(\frac{5}{x+7}+\frac{8}{2x+14}=\frac{3}{2}\)
r) \(\frac{x-1}{x}=\frac{1}{x+1}=\frac{2x-1}{x^2+x}\)
a, (x-1)3 - x(x-1)2 = 5(2-x) - 11(x+2)
b, (x-2)3 + (3x-1)(3x+1) = (x+1)3
c, \(\frac{2x-1}{5}-\frac{x-2}{3}=\frac{x+7}{5}\)
d, \(\frac{2\left(x-3\right)}{7}+\frac{x-5}{3}=\frac{13x+4}{21}\)
e, \(\frac{\left(x+10\right)\left(x+4\right)}{12}-\frac{\left(x+4\right)\left(2-x\right)}{4}=\frac{\left(x+10\right)\left(x-2\right)}{3}\)
Bµi 5: Gi¶i PT sau.
\(a,\frac{5x-2}{2-2x}+\frac{2x-1}{2}+\frac{x^2+x-3}{1-x}=1\)
b,\(\frac{6x-1}{2-x}+\frac{9x+4}{x+2}=\frac{3x^2-2x+1}{x^2-4}\)
\(c,\frac{1}{x-1}+\frac{2x^2-5}{x^3-1}=\frac{4}{x^2+x+1}\)
d) (x2 + 4x + 8)2 + 3x(x2 + 4x + 8) + 2x2 = 0
e) x4 + 2x3 + 4x2 + 2x + 1 = 0
\(f,\frac{3x-1}{x-1}-\frac{2x+5}{x+3}+\frac{4}{x^2+2x-3}=1\)
\(\frac{6}{x^2-1}+5=\frac{8x-1}{4x+4}-\frac{12x-1}{4-4x}\)
\(\frac{x+4}{x^2-3x+2}-\frac{x+1}{x^2-4x+3}=\frac{2x+5}{x^2-4x+3}\)
